1. Field of the Invention
The present invention relates to symbol timing estimation in communication systems, for example orthogonal frequency division multiplexing systems.
2. Description of the Related Art
Orthogonal frequency division multiplexing (OFDM) has been proposed for use in high bit-rate wireless applications in multi-path radio environments. OFDM can enable such applications without a high complexity receiver. OFDM is required by wireless local area network (WLAN), digital video broadcasting (DVB) and broadband wireless access (BWA) standards and is a strong candidate for some of the 4G wireless technologies.
OFDM is a multicarrier block transmission system. A block of N symbols are grouped together and sent in parallel. There is no interference among the data symbols sent in a block. In the transmitter, samples of the multicarrier signal can be obtained using an inverse fast fourier transform (IFFT) of the data symbols. A fast fourier transform (FFT) can be used in the receiver to obtain the data symbols. There is no need for N oscillators, filters and so on.
The popularity of OFDM stems from the use of IFFT/FFT in the transmitter and receiver respectively, these having efficient implementations.
FIG. 1(A) shows an example of a signal transmitted from the transmitter in an OFDM system. The transmitted signal comprises a succession of time domain symbols OS1, OS2 and OS3. In a multipath environment, the transmitted signal reflects off several objects before reaching the receiver, with the result that multiple delayed versions of the same signal arrive at the receiver. This delay spread causes distortion of the transmitted signal known as intersymbol interference (ISI), as shown in FIG. 1(B).
To try to prevent this intersymbol interference, it has been proposed to insert a guard interval between successive ones of the symbols in the transmitted signal. Although zeros could be inserted into the guard interval to alleviate the ISI problem, orthogonality of the carriers is lost when multipath channels are involved. Accordingly, to restore the orthogonality it has been proposed to include a cyclic prefix (CP) or cyclic prefix extension (CPE), in the guard interval, as shown in FIG. 2.
As shown in FIG. 2, an original OFDM symbol OS comprises N symbol samples and has a useful symbol period Tu. The last L symbol samples of the symbol are copied into the guard interval at the beginning of the symbol. In this way, for each symbol the same series of L symbol samples appears originally in the guard interval and then again, N symbol samples after its original appearance, at the end of the symbol. For example, Tu may be 13.05 μs, N may be 1024 and L may be 200, so that the guard interval duration is 2.55 μs.
The effect of the insertion of the cyclic prefix extension in a multipath environment is illustrated in FIG. 3. As shown in FIG. 3, a signal having two consecutive symbols OS1 and OS2, each with a CPE, is transmitted by the transmitter. FIG. 3 shows that four different versions of the transmitted signal arrive at the receiver with different delays. Provided that the CPE is longer than the maximum channel delay profile, it can be effective to prevent intersymbol interference. The effect of the CPE is to convert a linear convolution channel into a circular convolution channel, which restores the orthogonality at the receiver. However, energy is wasted in the cyclic prefix samples.
FIG. 4 shows an example of an OFDM system employing the cyclic prefix extension to reduce intersymbol interference. The system comprises a transmitter 1, a receiver 2, and a multi-path radio channel 3 which links the transmitter 1 to the receiver 2.
In the transmitter 1 data to be transmitted 10 is subjected to coding in a coding block 12, for example Turbo coding with a coding rate of ½ or ¾, and the coded transmission data is then subjected to a predetermined modulation, for example quadrature phase shift keying QPSK in a modulator 14 to obtain a series of data symbols DS. Also, a pilot symbol insertion block 16 produces, from time to time, pilot symbols PS to be sent with the data symbols DS to the receiver. A multiplexer 18 receives the data symbols DS and the pilot symbols PS and combines them into a single stream of symbols used to modulate the spectrum. This single stream of symbols is subject to serial-to-parallel conversion in a serial-to-parallel converter block 20, and the resulting block of parallel data is subject to an inverse fast fourier transform process in an IFFT block 22. The output of the IFFT block 22 comprises a series of time domain symbols TDS.
Next, each time domain symbol TDS has a cyclic prefix extension inserted at the beginning of the symbol by a CPE insertion block 24. The time domain symbols having respective CPEs are then converted into an analog signal by a digital-to-analog converter (DAC) 26 and are then up-converted into radio frequency (RF) signals by an RF block 27. The RF signal is transmitted to the receiver via the channel 3.
In the receiver 2, the RF signal received from the transmitter is down-converted into a baseband signal by an RF section 28. The baseband analog signal is converted into a corresponding digital signal by an analog-to-digital converter (ADC) 30. This digital signal comprises successive time domain symbols TDS. These time domain symbols TDS are supplied to a CPE removing block 34 and a symbol timing and frequency synchronisation block 36. The symbol timing and frequency synchronisation block 36 determines a symbol timing point STP for each time domain symbol TDS and supplies this symbol timing point STP to the CPE removing block 34. The CPE removing block 34 then removes from each TDS its CPE. The series of time domain symbols TDS with the CPEs removed is then applied to a FFT block 38 which applies FFT processing to the symbols to derive therefrom the original data symbols DS and pilot symbols PS.
These data symbols and pilot symbols are subject to parallel-to-serial conversion in a parallel-to-serial converter 40. The data symbols DS are then separated from the pilot symbols PS by a demultiplexer 42. The pilot symbols PS are supplied to a channel estimation block 44 which performs channel estimation based on the pilot symbols. A channel estimate CE obtained by the channel estimation block 44 is supplied to a demodulator 46 which also receives the data symbols DS. The demodulator 46 demodulates the data symbols DS and then supplies the demodulated symbols to a decoding block 48 which decodes the demodulator symbols to produce reconstructed data 50 which is output from the receiver.
FIG. 5 shows a conventional implementation of the symbol timing and frequency synchronisation block 36 in the receiver 2 of FIG. 4. In this implementation, successive symbol samples rk of the received time domain symbols TDS are applied to an input I. The samples rk are applied to a first input of a complex multiplier 362. The samples rk are also applied to an input of a delay block 364 which delays the samples by N samples to produce a stream of delayed samples rk+N. Here, as described previously, N is the number of samples per OFDM symbol prior to CPE insretion. The delayed samples rk+N are subject to conjugation by a conjugation block 366 to produce conjugated samples r*k+N which are applied to a further input of the complex multiplier 362. The output rkr*k+N of the multiplier 362 is applied to an input of a moving summation block 368 which produces a moving sum of L samples of the output of the multiplier 362. Here, as described previously, L is the number of samples in the CPE. This moving sum γ(d) is a correlation function representing the autocorrelation of a first series of L samples, starting with sample d and ending with sample d+L−1, and a second series of L samples starting with sample d+N and ending with sample d+N+L−1. Here, d is a sample index. In other words
      γ    ⁢                  ⁢          (      d      )        =            ∑              k        =        d                    d        +        L        -        1              ⁢                  ⁢                  r        k            ⁢                        r                      k            +            N                    *                .            This correlation function γ(d) will have a peak value when the first series of L samples coincides with the CPE and the second series of samples coincides with the last L samples of the symbol. In this way, the peak value of the correlation function γ(d) can be used to detect the symbol timing.
In order to identify the peak reliably, the correlation function γ(d) is subjected to normalisation to obtain a normalised measure MCP(d) for symbol timing estimation. To carry out this normalisation, an energy R(d) of the cyclic prefix portion is calculated according to the formula
      R    ⁢                  ⁢          (      d      )        =            1      2        ⁢                  ∑                  k          =          d                          d          +          L          -          1                    ⁢                          ⁢                        (                                                                                      r                  k                                                            2                        +                                                                            r                                      k                    +                    N                                                                              2                                )                .            In FIG. 5, an energy |rk|2 of each sample rk is calculated by a first squarer 370, and an energy |rk+N|2 of each delayed sample rk+N is calculated by a second squarer 372. The outputs of the first and second squarers 370 and 372 are summed by an adder 374, and the sum |rk|2+|rk+N|2 of the sample energies is then subjected to a moving summation by a moving summation block 376. As in the case of the moving summation block 368, the moving sum comprises L successive rk samples and L successive delayed samples rk+N. The moving sum produced by the moving summation block 376 is then halved by a multiplier 378 to produce the energy R(d). This energy R(d) is then squared by a squarer 380 and the result R2(d) is applied to one input of a divider 382.
The correlation function γ(d) is also subjected to squaring by a further squarer 384 and the result |γ(d)|2 is applied to the other input of the divider 382. Thus, the divider 382 produces at its output the normalised measure MCP(d) for symbol timing estimation, where
            M      CP        ⁡          (      d      )        =                                                    γ            ⁢                                                  ⁢                          (              d              )                                                2                              R          2                ⁡                  (          d          )                      .  A symbol timing estimate (STP in FIG. 4) is taken to be the point in time when MCP(d) has a peak value in the symbol period.
A trigger circuit 386 is also triggered upon detecting the peak value in the normalised measure MCP(d). At this time, the correlation function γ(d) is applied to a phase detector 388 which detects a phase angle of the correlation function. This phase angle is divided by −2π by a multiplier 390 to produce a measure
  Δ  ⁢            f      ^        CP  for frequency offset estimation, where
      Δ    ⁢                  f        ^            CP        =            -              1                  2          ⁢          π                      ⁢    ∠γ    ⁢                  ⁢                  (        d        )            .      
The accuracy of the symbol timing estimate and the frequency offset measure can have a significant effect on performance of the OFDM system. For example, the frequency offset can influence orthogonality of subcarriers, and loss of orthoganality in turn leads to intercarrier interference.
In the FIG. 5 implementation the measure MCP(d) provides a good timing estimate when the power of the first path in a multipath environment is the largest. However, when delayed paths have more power than the first significant path, the measure does not provide a good estimate for symbol timing. In such cases, the measure MCP(d) will have a peak for the strongest delayed path and will set this as the symbol timing point.
FIGS. 6(A) to 6(D) illustrate schematically the variation of the measure MCP(d) with the sample index over a symbol period. FIGS. 6(A) and 6(B) both illustrate the variation under line-of-sight (LO) conditions. In FIG. 6(A) it is assumed that there is a single dominant path. In this case, the measure MCP(d) has a single peak from which the symbol timing can be taken. In the case of FIG. 6(B) there are two paths, the first path having a higher energy than the second (delayed) path. In this case the measure MCP(d) corresponds to the superposition of both paths. However, since the first path is stronger than the second path, the peak in the measure MCP(d) still constitutes the correct symbol timing point.
FIGS. 6(C) and 6(D) illustrate the variation of MCP(d) under non-line-of-sight (NLO) conditions. In FIG. 6(C) a first path has less energy than a second (delayed) path but the first path is still significant. The measure MCP(d) is represented by the superposition of both paths, as in FIG. 6(B). In this case, however, the peak in MCP(d) corresponds to the timing of the second path, which provides the wrong symbol timing. A similar situation applies in FIG. 6(D). In this case, the first and second (delayed) paths have the same energy and this causes the measure MCP(d) to have a plateau region. It is difficult to determine the symbol timing point reliably from this plateau region, because there will usually be significant noise in the measure so that the plateau region will not be completely flat.
It is therefore desirable to provide an improved method and apparatus for obtaining a symbol timing estimate which can work over a wider range of channel conditions. In particular, it is desirable to detect the first significant path reliably in a multipath environment, even if there are delayed paths of higher energy.